String theory is designed to combine all our knowledge of the universe and explain it. When she appeared, she literally fascinated with her seeming simplicity and brevity, uniting what previously seemed impossible. However, over time it became clear that this beautiful theory only seems simple and, to the great regret of many researchers, gives rise to much more questions than answers. This theory describes one-dimensional, vibrating fibrous objects called "strings" that propagate through spacetime and interact with each other. Despite the fact that today other theories are popular among physicists, scientists gradually, piece by piece, continue to discover and decipher the fundamental strings of the physical Universe using mathematical models. So, according to a new study, mathematicians at the University of Utah have found new evidence for string theory.
In string theory, creation is like incredibly small, vibrating strands of energy that can twist, stretch, and contract. Theoretical physicists believe that everything that exists consists of strings, but no one has been able to verify this by experimental methods so far.
The strings of the universe
By skillfully combining the ideas of quantum mechanics and general relativity (GR), the string theory, physicists believe, should build a future theory of gravity. However, today, scientists increasingly criticize string theory and pay less attention to it due to the huge number of questions that it raises. However, according to a new study published in Letters in Mathematical Physics, string theory still has a right to exist.
Mathematicians from the University of Utah and St. Louis University have published mathematical calculations on two branches of string theory. In the course of their work, the researchers studied a special family of compact K3 surfaces - connected complex two-dimensional surfaces. They are important geometric tools for understanding the symmetries of physical theories.
An example of a 3-dimensional cross-section of a K3 surface used by mathematicians to study string duality between F-theory and heterotic theory in eight dimensions.
Recall that one of the important features of string theory is that it requires extra dimensions of spacetime for mathematical consistency. However, not every way of processing these extra dimensions, also called “compactification,” gives a model with the correct properties to describe nature. For the so-called eight-dimensional compactification of a string theory model, called F-theory, the extra dimensions must have the shape of a K3 surface.
In the new work, the researchers examined the duality of two types of string theory - F-theory and heterotic - in eight dimensions.
String theory to be
The team found four unique ways to cut K3 surfaces in a particularly useful way, using Jacobian elliptical bundles - multi-fiber assemblies shaped like a loaf or donut. Researchers have constructed explicit equations for each of these bundles and have shown that string theory concepts in the real physical world have a right to exist.
Example of K3 surface
"You can think of this family of surfaces as a loaf of bread, and each vibration as a 'slice' of that loaf," the researchers write. By studying the sequence of "slices", we can visualize and better understand the entire loaf. An important part of this research, according to the authors, is to identify certain geometric building blocks, called “dividers,” within each K3 surface.
Hours of painstaking work, as a result, allowed mathematicians to prove theorems for each of the four bundles, and then push each theorem through complex algebraic formulas. SciTechDaily cites the study's authors that for the last part of this process, scientists used Maple software and a specialized differential geometry package that optimized the computational effort.
Our universe is very strange and possibly made of strings.
Note that since the 1980s, string theory has spawned as many as five versions of its own. And although each of them is built on strings and extra dimensions (all five versions are combined into a general superstring theory, as my colleague Ilya Khel wrote about in detail), in detail these versions diverged quite a bit.
The paradox is that all five versions today can be called equally true. However, no one has succeeded in proving the existence of strings experimentally. And yet, despite all the skepticism and criticism of string theory, the new work proves its right to exist. Thus, string theory cannot be excluded from the list of potential candidates for the Theory of Everything - a universal theory that unites all our knowledge of the world and the Universe.